Abstract
Magnetotransport theory of layered superconductors in the flux flow steady state is revisited. Longstanding controversies concerning observed Hall sign reversals are resolved. The conductivity separates into a Bardeen-Stephen vortex core contribution, and a Hall conductivity due to moving vortex charge. This charge, which is responsible for Hall anomaly, diverges logarithmically at weak magnetic field. Its values can be extracted from magetoresistivity data by extrapolation of vortex core Hall angle from the normal phase. Hall anomalies in YBa_22Cu_33O_{7}7, Bi_22Sr_22CaCu_22O_{8-x}8−x, and Nd_{1.85}1.85Ce_{0.15}0.15CuO_{4-y}4−y data are consistent with theoretical estimates based on doping dependence of London penetration depths. In the appendices, we derive the Streda formula for the hydrodynamical Hall conductivity, and refute previously assumed relevance of Galilean symmetry to Hall anomalies.
Highlights
Vortex dynamics approaches calculate the vortex velocity as a response to the force exerted by a bias current, in addition to other forces
Conductivities can only be methodically computed by Kubo formulas, where the current is derived as a response to an applied electric field, and not vice versa
While the friction term can be derived from the longitudinal core conductivity by equating the Joule power dissipation [1], non-dissipative forces have been difficult to justify microscopically [39]
Summary
The Hall effect in the flux flow (FF) regime of superconducting films has long been an intriguing and controversial subject. We take on the Hall anomaly problem with a new approach to flux flow transport theory. This approach allows us to show that an additional Hall current is carried by moving vortex charge (MVC), which does not vanish in a layered superconductor geometry. The MVC can be estimated from independently measured thermodynamic coefficients, and Figure 1: Bardeen Stephen theory and Hall anomaly in the flux flow regime. For this illustration, vortex cores are assumed to obey Drude theory of metals. The paper ends with a summary of our results and their comparison to previous theories
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